Titlebook: Introduction to Stochastic Calculus; Rajeeva L. Karandikar,B. V. Rao Textbook 2018 Springer Nature Singapore Pte Ltd. 2018 Stochastic Calc

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,The Ito’s Integral,We begin this chapter with the quadratic variation and Levy’s characterization of the Brownian motion. Later, we will outline the basic development of the Ito’s Integral w.r.t. Brownian motion. We also discuss existence and uniqueness of solutions to the classical stochastic differential equations driven by Brownian motion.

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Dominating Process of a Semimartingale,In Chap. ., we saw that using random time change, any continuous semimartingale can be transformed into a amenable semimartingale, and then one can have a growth estimate on the stochastic integral similar to the one satisfied by integrals w.r.t. Brownian motion.

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SDE Driven by r.c.l.l. Semimartingales,In this chapter, we will consider stochastic differential equations as in Sect. . where the driving semimartingale need not be continuous.

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